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Problems
Contests
National and Regional Contests
Canada Contests
Canada National Olympiad
1987 Canada National Olympiad
2
2
Part of
1987 Canada National Olympiad
Problems
(1)
All ways of representing 1987 in another base [Canada 1987]
Source:
9/30/2011
The number 1987 can be written as a three digit number
x
y
z
xyz
x
yz
in some base
b
b
b
. If
x
+
y
+
z
=
1
+
9
+
8
+
7
x + y + z = 1 + 9 + 8 + 7
x
+
y
+
z
=
1
+
9
+
8
+
7
, determine all possible values of
x
x
x
,
y
y
y
,
z
z
z
,
b
b
b
.